1. Field of the Invention
The present invention relates to a simulation method for estimating the performance of a product made of a viscoelastic material. More particularly, the present invention relates to a simulation method for accurately estimating the performance of the product made of the viscoelastic material by means of a simulation.
2. Description of the Related Art
A viscoelastic material represented by a macromolecular material such as rubber or elastomer is widely applied to various products such as tires, balls for sports, rolls for printing machines.
It is expensive and takes much time to make a trial manufacture. Thus to save cost and time, simulation is made in various industrial fields to develop various products made of the viscoelastic material or a metal material. For example, to estimate the restitution performance of a golf ball, simulation methods of actual hitting tests are proposed.
To conduct the simulation, physical-property values such as the rigidity, viscosity, and the like of a material measured by a viscoelastic spectrum meter and physical-property values such as a modulus of direct elasticity (Young""s modulus) of a constituting material of a ball measured by a tension tester are used as input data in the simulation. In particular, because the viscoelastic spectrum meter measures the physical-property values of a dynamic strain-applied specimen, the viscoelastic spectrum meter is useful for simulating products made of the viscoelastic material.
However in measurement conducted by using the viscoelastic spectrum meter and the tension tester for measuring the modulus of direct elasticity, a large deformation amount cannot be imparted to the specimen. Thus a maximum strain speed applied to the specimen made of the viscoelastic material at a measuring time is as low as 0.001/s to 1.0/s and a maximum compression strain is also as low as 0.0001 to 0.02.
A product made of the viscoelastic material may deform rapidly and greatly owing to the influence of an external force applied thereto when it is actually used. For example, when a golf ball is hit, a maximum strain speed of a material for the golf ball is as high as 500/s to 5000/s and a maximum compression strain thereof is as large as 0.05-0.50.
As described above, the viscoelastic spectrum meter and the tension tester for measuring the modulus of direct elasticity are incapable of measuring the physical-property values of the viscoelastic material in a state equivalent to a condition where the product made of the viscoelastic material deforms quickly and greatly when it is actually used. Thus the maximum strain speed of the viscoelastic material and its maximum compression strain measured at a simulation time are much different from those measured at the time when the product made of it is actually used. Therefore the conventional simulation method of inputting the physical-property value obtained by using the viscoelastic spectrum meter and the tension tester is incapable of accomplishing an accurate simulation by taking the physical property of the viscoelastic material into consideration.
That is, it is known that the deformation behavior of the viscoelastic material when an impact load is applied thereto is different from that of the viscoelastic material when a static load is applied thereto. That is, the deformation behavior of the viscoelastic material is greatly influenced by a deformation amount or a deformation speed. In particular, when a macromolecular material such as rubber and elastomer is subjected to the impact load, it deforms at a speed as high as several seconds by 10000 or several seconds by 1000 and as greatly as by several tens of percentages in a quantitative respect. There are many viscoelastic materials that deform at such a high speed and in such a large amount. To develop products efficiently, there is a demand for conducting an accurate simulation. More specifically, the performance of a product such the golf ball depends on a dynamic behavior in a condition where it deforms greatly and quickly upon application of an impact thereto when it is hit. The performance of the product also depends on the characteristic of the material thereof. Therefore to develop a product, it is indispensable to conduct an accurate simulation in a condition equivalent to a condition in which the product made of the material is actually used.
Some viscoelastic materials change in the physical properties thereof such as the loss factor, rigidity (modulus of direct elasticity), and the like in dependence on the magnitude of a strain and a strain speed when an external force such as an impact load is applied thereto. That is, the viscoelastic material is diverse in its deformation speed and deformation magnitude. Thus depending on the deformation speed and the deformation magnitude, the physical property of the viscoelastic material has a property that it changes not linearly but nonlinearly. More specifically, as the viscoelastic material is deformed by an external force applied thereto and strained increasingly, the loop area of an S-S (strain-stress) curve increases and the physical properties such as the loss factor thereof change owing to a deformation state (speed and magnitude of deformation) thereof, thus showing nonlinearity in its property. Many viscoelastic materials have a high nonlinearity in their properties. Thus there is a demand for conducting an accurate simulation for a product made of such a viscoelastic material.
However there are no methods capable of accurately expressing a phenomenon that the physical property of the viscoelastic material, for example, its loss factor changes nonlinearly in a high extent in dependence on the deformation speed of and deformation magnitude thereof. Simulations have been hitherto conducted on the assumption that the physical-property value of the viscoelastic material composing the golf ball or the like hardly changes. Consequently the conventional simulation method has a disadvantage that it is incapable of correctly estimating the performance of the product made of the viscoelastic material in an actual use. Thus to estimate the performance of the product, trial manufacture cannot but be made.
The present invention has been made in view of the above-described situation. Thus, it is an object of the present invention to provide a simulation method of accurately estimating the performance of a product made of a viscoelastic material showing a nonlinearity in its property in a condition in which the product is actually used.
To achieve the object, according to the present invention, there is provided a simulation method for estimating performance of a product made of a viscoelastic material, comprising the steps of measuring a value of a strain, a strain speed, and a stress generated in the viscoelastic material momently in a measuring condition equivalent to a state in which the product is actually used; deriving time history data of a viscosity resistance of the viscoelastic material from time history data of the strain, the strain speed, and the stress and a viscoelastic model set in consideration of a viscosity of the viscoelastic material; and setting the product made of the viscoelastic material as a product model whose performance is analyzed and inputting a relationship among the strain, the strain speed, and the viscosity resistance to the product model to conduct a simulation in consideration of a phenomenon that the viscosity resistance changes in dependence on a variation of the strain and the strain speed. Thereby the performance of the viscoelastic model made of the viscoelastic material is estimated.
In the first aspect of the present invention, using the viscoelastic model set in consideration of the viscosity of the viscoelastic material, the simulation is conducted by deriving the viscosity resistance of the viscoelastic material and inputting the relationship among the strain, the strain speed, and the viscosity resistance to the product model. Therefore it is possible to accurately express a phenomenon that the physical property of the viscoelastic material changes nonlinearly with its deformation speed and deformation magnitude. Further because the value of each of the strain, the strain speed, and the strain is measured in a measuring condition equivalent to a state in which the product made of the viscoelastic material is actually used, it is possible to conduct a simulation in correspondence to various deformation states of the viscoelastic material. Accordingly it is possible to accurately estimate the performance of the product made of the viscoelastic material in which the relationship between the strain and the strain speed generated therein changes owing to a deformation state of the viscoelastic material and whose physical property such as a loss factor shows nonlinearity.
The time history data of the viscosity resistance of the viscoelastic material is derived from the time history data of each of the strain, the strain speed, and the stress and from the viscoelastic model set in consideration of the viscosity of the viscoelastic material. More specifically, from the viscoelastic model, the relationships among the strain, the strain speed, the modulus of direct elasticity, and the viscosity resistance are established as an equation respectively. In this manner, the viscosity resistance of the viscoelastic material is expressed as the function of the strain and the strain speed. The modulus of direct elasticity of the viscoelastic material is derived in correspondence to the strain and the stress, generated therein, obtained by the measurement. The value of the viscosity resistance is derived by substituting the modulus of direct elasticity, the strain, and the strain speed into the function. Since the time history data of each of the strain, the strain speed, and the stress is obtained by the measurement, time history data of the viscosity resistance corresponding to the strain and the strain speed can be obtained. As described above, the viscosity resistance is determined in dependence on the value of the strain and the strain speed and thus changes in correspondence to a variation of the strain and the strain speed that is made with the elapse of time.
The product made of the viscoelastic material is set as a product model whose performance is analyzed. The relationship among the strain, the strain speed, and the viscosity resistance is inputted to computation input data including the product model, a speed, a restriction condition, and the like to conduct a simulation in consideration of the phenomenon that the viscosity resistance changes in dependence on the variation of the strain and the strain speed.
The relationship among the strain, the strain speed, and the viscosity resistance is inputted to the product model at a computing time in the simulation. More specifically, two-dimensional data of the relationship between the strain and the strain speed and the relationship between the strain and the viscosity resistance are inputted to the product model for a computation. It is possible to input three-dimensional data of the relationship among the strain, the strain speed, and the viscosity resistance to the product model. That is, the data of the viscosity resistance can be inputted to the product model as the function of the strain and the strain speed to perform a computation.
In inputting the two-dimensional data of each of the relationship between the strain and the strain speed and the relationship between the strain and the viscosity resistance to the product model, the strain, the strain speed, and the viscosity resistance corresponding to the strain as well as the strain speed are written as input data by using the above-described relationships. More specifically, the strain, the strain speed, and the like are measured in a plurality of measuring conditions, and the relationship between the strain and the strain speed is recorded from time series data of the strain and the strain speed in each of different patterns having different measuring conditions. The value of the viscosity resistance corresponding to each curve is also recorded. By properly adjusting the relationship among the strain, the strain speed, and the viscosity resistance, the viscosity resistance at a given strain and a given strain speed is accurately derived for a computation.
In the second aspect of the present invention, there is provided a simulation method for estimating performance of a product made of a viscoelastic material, comprising the steps of measuring a value of a strain, a strain speed, and a stress generated in the viscoelastic material momently in a measuring condition equivalent to a state in which the product is actually used; computing a plurality of different moduli of direct elasticity from history data of the strain and that of the stress and deriving a relationship among the strain, the strain speed, and the modulus of direct elasticity; setting the product made of the viscoelastic material as a product model whose performance is analyzed and inputting the relationship among the strain, the strain speed, and the modulus of direct elasticity to the product model to conduct a simulation in consideration of a phenomenon that the modulus of direct elasticity changes in dependence on a variation of the strain and the strain speed. Thereby the performance of the viscoelastic model made of the viscoelastic material is estimated.
As described above, in the second aspect of the present invention, the rigidity (modulus of direct elasticity) of the viscoelastic material which changes in dependence on a deforming condition is computed from the time history data of the strain and the stress measured in the above-described measuring condition to conduct a simulation in consideration of the change of the modulus of direct elasticity corresponding to the variation of the strain and the strain speed. Therefore it is possible to accurately express the phenomenon that the physical property of the viscoelastic material changes nonlinearly in dependence on its deformation speed and deformation magnitude.
Further because the value of each of the strain, the strain speed, and the strain is measured in a measuring condition equivalent to a state in which the product made of the viscoelastic material is actually used, it is possible to conduct a simulation in correspondence to various deformation states of the viscoelastic material.
Accordingly it is possible to accurately estimate the performance of the product made of the viscoelastic material in which the relationship between the strain and the strain speed generated therein changes owing to a deformation state of the viscoelastic material and whose physical property such as a loss factor shows nonlinearity.
The modulus of direct elasticity shown by an inclination of a stress-strain curve is computed in each measuring condition from the time history data of each of the stress and the strain to determine the modulus of direct elasticity corresponding to the strain and the strain speed. That is, an appropriate rigidity of the viscoelastic material can be expressed by changing the modulus of direct elasticity of a spring of the viscoelastic model in correspondence to the strain and the strain speed.
The time history data of the viscosity resistance of the viscoelastic material is derived from the time history data of each of the strain, the strain speed, and the stress, the modulus of direct elasticity corresponding to the strain and the strain speed, and the viscoelastic model set in consideration of the viscosity of the viscoelastic material. More specifically, the relationships among the strain, the strain speed, the modulus of direct elasticity, and the viscosity resistance are established as an equation respectively. In this operation, the modulus of direct elasticity is found in correspondence to the strain and the strain speed, and the viscosity resistance is expressed as the function of the strain, the strain speed, and the modulus of direct elasticity. The value of the viscosity resistance is derived in consideration of the variation of the modulus of direct elasticity by substituting the modulus of direct elasticity, the strain, and the strain speed, and the modulus of direct elasticity into the function. Since the time history data of each of the strain, the strain speed, and the stress is obtained, the time history data of the viscosity resistance corresponding to the strain and the strain speed can be obtained.
The product made of the viscoelastic material is set as a product model whose performance is analyzed. The relationship among the strain, the strain speed, and the modulus of direct elasticity is inputted to computation input data including the product model, a speed, a restriction condition, and the like to conduct a simulation in consideration of the phenomenon that the modulus of direct elasticity changes in dependence on the variation of the strain and the strain speed.
The relationship among the strain, the strain speed, and the modulus of direct elasticity is inputted to the product model at a computing time in the simulation. More specifically, two-dimensional data of the relationship between the strain and the strain speed and the relationship between the strain and the modulus of direct elasticity are inputted to the product model for a computation. It is possible to input three-dimensional data of the relationship among the strain, the strain speed, and the modulus of direct elasticity to the product model. That is, the data of the modulus of direct elasticity can be inputted to the product model as the function of the strain and the strain speed to perform a computation.
Based on the result of measurement and by using the above-described relationship, the strain, the strain speed, the modulus of direct elasticity corresponding to the strain as well as the strain speed, and the viscosity resistance are written as input data. More specifically, the strain, the strain speed, and the like are measured in a plurality of measuring conditions, and the relationship between the strain and the strain speed is recorded from time series data of the strain and the strain speed in each of different patterns having different measuring conditions. The value of the modulus of direct elasticity corresponding to each curve is also recorded. By computing the viscosity resistance momently from the value of each of the strain, the strain speed, and the modulus of direct elasticity, properly adjusting the relationship among the strain, the strain speed, and the modulus of direct elasticity, and including the relationship among them into the computation for the simulation, the physical-property value of the viscoelastic material at a given strain and a given strain speed is accurately derived for the computation.
In the third aspect of the present invention, there is provided a simulation method for estimating performance of a product made of a viscoelastic material, comprising the steps of measuring a value of a strain, a strain speed, and a stress generated in the viscoelastic material momently in a measuring condition equivalent to a state in which the product is actually used; deriving time history data of a viscosity resistance of the viscoelastic material separately in each of a strain increase state and a strain decrease state or a restoration state from time history data of the strain, the strain speed, and the stress and a viscoelastic model set in consideration of a viscosity of the viscoelastic material; setting the product made of the viscoelastic material as a product model whose performance is analyzed and inputting a relationship among the strain, the strain speed, and the viscosity resistance to the product model to conduct a simulation in consideration of a phenomenon that the viscosity resistance changes in dependence on a variation of the strain and the strain speed and in consideration of a difference in the viscosity resistance between a strain increase state and a strain decrease state or a restoration state. Thereby the performance of the viscoelastic model made of the viscoelastic material is estimated.
As described above, in the third aspect of the present invention, using the viscoelastic model set in consideration of the viscosity of the viscoelastic material, the simulation is conducted by deriving the viscosity resistance of the viscoelastic material separately in each of the strain increase state and the strain decrease state and inputting the relationship among the strain, the strain speed, and the viscosity resistance to the product model. Therefore it is possible to accurately express a phenomenon that the physical property of the viscoelastic material changes nonlinearly with its deformation speed and deformation magnitude. There is a case in which at an equal value of the strain, the value of the viscosity resistance in the strain increase state is different from the value thereof in the strain decrease state (or restoration state). Therefore the simulation can be accomplished with high precision by differentiating the value of the viscosity resistance in the strain increase state and that of the viscosity resistance in the strain decrease state or the restoration state from each other. Further because the value of each of the strain, the strain speed, and the strain is measured in a measuring condition equivalent to a state in which the product made of the viscoelastic material is actually used, it is possible to conduct a simulation in correspondence to various deformation states of the viscoelastic material. Accordingly it is possible to accurately estimate the performance of the product made of the viscoelastic material in which the relationship between the strain and the strain speed changes owing to a deformation state of the viscoelastic material and whose physical property such as a loss factor shows nonlinearity.
The time history data of the viscosity resistance of the viscoelastic material is derived separately in each of the strain increase state and the strain decrease state or the restoration state from the time history data of each of the strain, the strain speed, and the stress and from the viscoelastic model set in consideration of the viscosity of the viscoelastic material. More specifically, the relationships among the strain, the strain speed, the modulus of direct elasticity, and the viscosity resistance are established as an equation respectively. In this manner, the viscosity resistance is expressed as the function of the strain and the strain speed by differentiating the value of the viscosity resistance in the strain increase state from that of the viscosity resistance in the strain decrease state or the restoration state. The modulus of direct elasticity of the viscoelastic material is derived in correspondence to the strain and the stress, generated therein, obtained by the measurement. The value of the viscosity resistance is derived by substituting the modulus of direct elasticity, the strain, and the strain speed into the function. Since the time history data of each of the strain, the strain speed, and the stress is obtained, the time history data of the viscosity resistance corresponding to the strain and the strain speed can be obtained. As described above, the viscosity resistance is determined in dependence on the value of the strain and the strain speed and thus changes in correspondence to the variation of the strain and the strain speed which is made with the elapse of time. The deformation state generated in the viscoelastic material can be divided into the xe2x80x9cstrain increase statexe2x80x9d in which the strain increases in the compression direction thereof and the xe2x80x9crestoration statexe2x80x9d in which the compression amount thereof decreases gradually. Therefore the simulation is conducted separately in each of the strain increase state and the strain decrease state (or restoration state). Depending on a case, the deformation state generated in the viscoelastic material can be divided into a stress-applied state and a stress-eliminated state.
The product made of the viscoelastic material is set as a product model whose performance is analyzed. The relationship among the strain, the strain speed, and the viscosity resistance is inputted to computation input data including the product model, a speed, a restriction condition, and the like to conduct a simulation in consideration of the phenomenon that the viscosity resistance changes in dependence on the variation of the strain and the strain speed and in consideration of the difference in the viscosity resistance between the strain increase state and the strain decrease state or the restoration state.
The relationship among the strain, the strain speed, and the viscosity resistance is inputted to the product model at a computing time in the simulation. More specifically, two-dimensional data of the relationship between the strain and the strain speed and the relationship between the strain and the viscosity resistance are inputted to the product model for a computation. It is possible to input three-dimensional data of the relationship among the strain, the strain speed, and the viscosity resistance to the product model. That is, the data of the viscosity resistance can be inputted to the product model as the function of the strain and the strain speed to perform a computation.
In inputting the two-dimensional data of each of the relationship between the strain and the strain speed and the relationship between the strain and the viscosity resistance to the product model, the strain, the strain speed, and the viscosity resistance, corresponding to the strain as well as the strain speed, different in its value between the strain increase state and the strain decrease state or the restoration state are written as input data by using the above-described relationships. More specifically, the strain, the strain speed, and the like are measured in a plurality of measuring conditions, and the relationship between the strain and the strain speed is recorded from time series data of the strain and the strain speed in each of different patterns having different measuring conditions. The value of the viscosity resistance corresponding to each curve is also recorded. By properly adjusting the relationship among the strain, the strain speed, and the viscosity resistance, the viscosity resistance at a given strain and a given strain speed is accurately derived for a computation.
In the simulation method of the first, second, third aspects of the present invention, the value of each of the strain, the strain speed, and the stress generated in the product made of the viscoelastic material is measured momently in a measuring condition equivalent to a state in which the product is actually used. More specifically, the measuring condition is set equivalently to a state in which a product made of the viscoelastic material is actually used and deforms owing to an external force applied to the product. The value of each of the strain, the strain speed, and the stress generated in the product made of the viscoelastic material is measured momently in the above-described measuring condition to obtain the time history data of each of the strain, the strain speed, and the stress. Thus it is possible to obtain the information of a deformation state of the viscoelastic material, assuming that the product made of the viscoelastic material is actually used and an external force is applied to the product. Thereby it is possible to correctly estimate the property of the, viscoelastic material which deforms greatly and quickly when it is subjected to an impact load.
It is preferable to measure the value of each of the strain, the strain speed, and the stress momently in a plurality of measuring conditions. By altering the magnitude of the external force applied to the product made of the viscoelastic material and setting a plurality of measuring conditions, it is possible to obtain data of various patterns about the strain, the strain speed, and the stress and improve the accuracy of input values in the simulation. To obtain data with possible largest number of patterns, it is preferable to measure the value of each the strain, the strain speed, and the stress from a time when the stain is generated in the viscoelastic material upon application of an external force until the strain becomes approximately zero. It is also preferable to measure the values thereof at short intervals.
It is preferable to compose the viscoelastic model of a spring and a dashpot in view of the viscosity of the viscoelastic material. Such a viscoelastic model simplifies the viscosity of the viscoelastic material, it is easy to consider the influence of the viscosity on a deformation state of the viscoelastic material. More specifically, a maxwell model, Voight model, and a combination of a plurality of springs and dashpots are favorable. To simplify the construction of the viscoelastic model, a two-component model is favorable. These viscoelastic material models are used in such a way that the viscosity resistance of the dashpot and the rigidity of the spring (modulus of direct elasticity E or shear coefficient) are variable. The shear coefficient is a physical-property value determined by the modulus of direct elasticity (Young""s modulus) E and Poisson""s ratio.
The more the number of measuring conditions is, the more accurately the physical property of the viscoelastic material can be realized in a condition in which different strains and strain speeds are measured. Thus it is preferable to measure the strain, the strain speed, and the like in a plurality of different measuring conditions. However the more the number of the measuring conditions is, the more it takes to perform a computation in conducting the simulation. In the case of a strain and a strain speed not the same as the data of the strain and the strain speed measured under a predetermined measuring condition, it is preferable to compute the modulus of direct elasticity by using an interpolation. As the interpolation, a primary interpolation is performed by using a binary value of the modulus of direct elasticity determined in dependence on a strain and a strain speed close to the strain and the strain speed measured under the predetermined measuring condition or an interpolation which is performed by using values measured in all predetermined measuring conditions. By performing such an interpolating operation, it is possible to compute the viscosity resistance and the modulus of direct elasticity in correspondence to a variation, of the strain and the strain speed generated in the viscoelastic material, which is made according to measuring conditions.
The simulation method of the present invention allows a correct simulation of the property and deformation behavior of the viscoelastic material showing nonlinearity in its property, assuming that a product made of the viscoelastic material is actually used. By using the viscoelastic model whose viscosity resistance is determined by the value of the strain and the strain speed and computing its viscosity resistance, as described above in the characteristic of the first and third aspect of the present invention, it is possible to consider the nonlinearity of the viscoelastic material showing not linearity in its physical property but nonlinearity, namely, deforming according to its deformation speed and deformation magnitude. In particular, it is possible to accurately simulate the viscoelastic material whose loss factor shows a high nonlinearity and thereby estimate the performance of a product made of the viscoelastic material, assuming that the product is actually used. By using the viscoelastic model whose modulus of direct elasticity is determined by the value of the strain and the strain speed, as described above in the characteristic of the second aspect of the present invention, it is possible to accurately simulate the viscoelastic material whose modulus of direct elasticity shows the nonlinearity and thereby estimate the performance of a product made of the viscoelastic material, assuming that the product is actually used.
It is preferable to conduct the simulation method of the present invention by a finite element method.
In conducting the simulation method by the finite element method, a large number of nodal points and elements are set on the product model. That is, in estimating the property of the viscoelastic material composing a product by simulating the product by the finite element method, the modulus of direct elasticity of a spring of the viscoelastic model is determined by the strain and the strain speed generated in each element. Thereby for each element, it is possible to indicate the property of the viscoelastic material in a proper condition of a strain and a strain speed.
Needless to say, instead of the modulus of direct elasticity, a shear coefficient may be used in relation to the Poisson""s ratio. Whether the modulus of direct elasticity or the shear coefficient is used depends on the specification of the program of the finite element method.
The strain, the strain speed, and the stress are measured by a split Hopkinson""s bar tester. The split Hopkinson""s bar tester is capable of straining a specimen very quickly and greatly. That is, owing to the use of the split Hopkinson""s bar tester, it is possible to obtain time series data of each of the strain, the strain speed, and the stress of the viscoelastic material in a measuring condition in which the viscoelastic material deforms by several tens of percentages at a speed as high as several seconds by 10000 or several seconds by 1000 and as great as by several tens of percentages in a quantitative respect. Assuming the condition of a strain and a strain speed generated in the specimen by the split Hopkinson""s bar tester is equivalent to a condition of a strain and a strain speed generated in the viscoelastic material when an impact load is applied to a product made of the viscoelastic material, it is possible to obtain physical properties of the viscoelastic material in correspondence to various states such as a state in which the viscoelastic material deforms very quickly and greatly. Thus by using the physical property measured by the split Hopkinson""s bar tester, the accuracy of the simulation can be improved.
The split Hopkinson""s bar tester is capable of measuring physical properties of the material composing the specimen in various regions of the strain and the strain speed by only altering the collision speed of its impact bar which applies an impact to the specimen. Therefore the split Hopkinson""s bar tester makes it possible to obtain the physical properties of the material in various strains and strain speeds.
The split Hopkinson""s bar tester is originally used to evaluate an impact behavior of a metal material. In the present invention, the split Hopkinson""s bar tester is improved in its construction to evaluate the viscoelastic material having viscosity. The method of measuring the physical property of a material by using the split Hopkinson""s bar tester will be described later.
Needless to say, the physical property of the material may be measured by a measuring method other than the method carried out by using the split Hopkinson""s bar, provided that a specimen can be deformed greatly at a high speed and the physical property of the material of the specimen can be measured in a measuring condition equivalent to a condition in which a product made of the material is actually used.
When a strain, a strain speed, and a stress generated in a viscoelastic material are measured in a measuring condition equivalent to a condition in which a product made of the viscoelastic material is actually used, a maximum value of the strain generated in the viscoelastic material is in the range of 0.05 to 0.50 and/or a maximum value of the strain speed is in the range of 500/s to 10000/s and favorably in the range of 500/s to 5000/s.
The range of the maximum value of the strain and that of the strain speed are the condition of the strain and the strain speed generated when the viscoelastic material deforms very quickly and greatly. Thus to estimate the performance of the product when it deforms very quickly and greatly, it is preferable to use time series data of each of the strain, the strain speed, and the stress in this condition.
The viscoelastic material is used for a golf ball. The product model is a golf ball. The golf ball is a product made of the viscoelastic material. When the golf ball is actually used, an external force such as an impact load is applied thereto and it deforms at a very high speed and in a large amount. The state of the golf ball deforming at a very high speed and in a large amount affects the performance of the golf ball in a high extent. Therefore the analysis based on the simulation method of the present invention is very useful for estimating the performance of the golf ball. The simulation method is capable of estimating the performance of the golf ball with high accuracy without making a trial manufacture. Thus the simulation method allows efficient designing of the golf ball.
A phenomenon of a collision between the golf ball and a hitting object assumed to be a golf club head is simulated to estimate the behavior of the golf ball at the time of the collision. The simulation method is capable of estimating the physical property of the viscoelastic material composing the golf ball, assuming that the viscoelastic material is subjected to a strain, a strain speed, and a stress equivalent to those generated in the viscoelastic material of the golf ball when it is actually hit with the golf club head. Therefore simulation method is capable of estimating the restitution coefficient of the golf ball and the behavior of the golf ball such as a deformation state thereof when it is hit.
The simulation method of the present invention is applicable to a so-called one-piece golf ball, a so-called two-piece golf ball made of a core made of cross-linked rubber and a cover covering the core, and a so-called multi-piece golf ball made of three or more layers. That is, the simulation method of the present invention is applicable to golf balls made of the viscoelastic material and having any constructions.
The viscoelastic material includes viscoelastic materials. For example, thermoplastic resin, thermosetting resin, elastomers, and rubber can be used. It is possible to use these viscoelastic materials singly or a mixture thereof. It is possible to add additives such as a colorant, a deterioration prevention agent, and a cross-linking agent to each of these viscoelastic materials and the mixture thereof as necessary. The simulation method is applicable to all materials so long as the strain, strain speed, and stress thereof can be measured in a condition where a product made of them is actually used.
As the viscoelastic material, it is possible to use synthetic resin such as ionomer which is used as a material for a golf ball, polybutadiene (butadiene rubber), natural rubber, polyisoprene, styrene-butadiene copolymer, ethylene-propylene-diene copolymer (EPDM), and urethane rubber.
As products made of the viscoelastic material, in addition to the golf ball, a rubber roller for a printing apparatus, a tire, and sports goods, for example, goods for tennis, golf, and the like are known. It is necessary that the viscoelastic material composes at least one part of a product. The viscoelastic material may be used in combination with other materials such as a metal material to form a composite-molded product. The simulation method is capable of estimating the performance of a portion, of the product, constructed of the viscoelastic material. The simulation method is preferably applicable to a product that deforms very quickly and greatly when it is subjected to an impact load. The simulation method is capable of estimating the performance of the product and its dynamic behavior with high accuracy.